Toward Consistent and Efficient Map-based Visual-inertial Localization: Theory Framework and Filter Design

Abstract

This paper focuses on designing a consistent and efficient filter for map-based visual-inertial localization. First, we propose a new Lie group with its algebra, based on which a novel invariant extended Kalman filter (invariant EKF) is designed. We theoretically prove that, when we do not consider the uncertainty of the map information, the proposed invariant EKF can naturally maintain the correct observability properties of the system. To consider the uncertainty of the map information, we introduce a Schmidt filter. With the Schmidt filter, the uncertainty of the map information can be taken into consideration to avoid over-confident estimation while the computation cost only increases linearly with the size of the map keyframes. In addition, we introduce an easily implemented observability-constrained technique because directly combining the invariant EKF with the Schmidt filter cannot maintain the correct observability properties of the system that considers the uncertainty of the map information. Finally, we validate our proposed system's high consistency, accuracy, and efficiency via extensive simulations and real-world experiments.

FEJ-VIRO: A Consistent First-Estimate Jacobian Visual-Inertial-Ranging Odometry

“…[23] proved the key cause of inconsistency is the gain of spurious information along unobservable directions, which results in the over-confidence of the estimator. Extensive works studied this problem and proposed many techniques to address it [25]. We refer the readers to [26] for detailed review.…”